Cut the aubergine into ¼ in / 0.5cm slices. Bring a large saucepan of water to the boil, lightly salted or not, as you prefer, and put in the aubergine slices. After 2–3 minutes, put in the courgettes and leeks and boil for a further 2 minutes. Lift out the vegetables with a slotted spoon, put them in a colander, and refresh under cold running water to stop them cooking any further. Put to dry on layers of kitchen paper: Cook the lasagne sheets according to the directions on the packet, a few sheets at a time, if necessary, in the same saucepan of water in which you cooked the vegetables. If using freshly made lasagne that is still soft and supple, cook for 2 minutes only. Lay the cooked lasagne sheets on a clean tea-towel.
Liberally oil a square or rectangular ovenproof dish, and spread some béchamel sauce on the bottom. Cover with a layer of lasagne sheets, then a layer of vegetables, then some mozzarella and ricotta, and some tomato sauce. Spoon on another layer of béchamel, top with another of lasagne, and so on, finishing with sheets of lasagne topped with the remaining béchamel sauce. Sprinkle with the grated Parmesan, and bake in a preheated oven at 180°C / 350°F / Mark 4 for 50–60 minutes. Turn up the heat for the last 10 minutes, if necessary, to brown the top. Serve very hot.